A major brokerage company has an office in Miami, Florida. The manager of the office is evaluated based on the number of new clients generated each quarter. The following data reflect the number of new customers added during each quarter between 2006 and 2009.
| 2006 | 2007 | 2008 | 2009 |
| 1st Quarter |
218 |
250 |
244 |
229 |
| 2nd Quarter |
190 |
220 |
228 |
221 |
| 3rd Quarter |
236 |
265 |
263 |
248 |
| 4th Quarter |
218 |
241 |
240 |
231 |
a. Plot the time series and discuss the components that are present in the data.
b. Referring to part a, fit a linear trend model to the data for the years 2006- 2008. Then use the resulting model to forecast the number of new brokerage customers for each quarter in the year 2009. Compute the MAD and MSE for these forecasts and discuss the results.
c. Using the data for the years 2006-2008, determine the seasonal indexes for each quarter.
d. Develop a seasonally unadjusted forecast for the four quarters of year 2009.
e. Using the seasonal indexes computed in part d; determine the seasonally adjusted forecast for each quarter for the year 2009. Compute the MAD and MSE for these forecasts.
f. Examine the values for the MAD and MSE in parts b and e. Which of the two forecasting techniques would you recommend the manager to use in order to forecast the number of new clients generated each quarter? Support your choice by explaining your rationale.